**Biographical note of the Editor-in-Chief:**

**Jie Xiao**

PhD Peking, 1992

Alexander von Humboldt Research Fellow, 1999

Dean of Science Distinguished Scholar Medal, 2009

Dr. **Jie Xiao** Dr. Xiao's research and teaching interests lie in geometric analysis and partial differential equations. In particular, Dr. Xiao works on the interactions between harmonic analysis, complex variables and operator theory, but also applies techniques coming from function spaces and potential theory to the study of conformal-convex-differential geometry and heat-type equations and Navier-Stokes equations.

Here are some of his recent articles:

- P-capacity vs surface-area, Adv. Math. 208(2017)1318-1336
- Isoperimetry for semilinear torsion problems in Riemannian two-manifolds, Adv. Math. 229(2012)2379-2404
- Toward best isoperimetric constants for (H1,BMO)-normal conformal metrics on Rn, n>=3, Adv. Math. 220(2009)540-559
- The Qp Carleson measure problem, Adv. Math. 217(2008)2075-2088.
- Sharp Sobolev and isoperimetric inequalities split twice, Adv. Math. 211(2007)417-435
- Homogeneous endpoint Besov space embeddings by Hausdorff capacity and heat equation, Adv. Math. 207(2006)828-846

Meanwhile, Dr. Xiao is the author of the following monographs and texts:

- Qa Analysis on Euclidean Spaces, De Gruyter, 2019
- Gaussian Capacity Analysis (with L. Liu-D. Yang-W. Yuan), Lecture Notes in Math. 2225, Springer-Verlag, 2018
- Integral and Functional Analysis, Nova Science Publishers, 2008
- Geometric Qp Functions, Frontiers in Math., Birkhauser-Verlag, 2006
- Elementary Number Theory, International Press, 2006.
- Holomorphic Q Classes, Lecture Notes in Math. 1767, Springer-Verlag, 2001

In addition, Dr. Xiao serves as:

- Editor-in-Chief of the Advances in Analysis and Geometry, 2018 - present
- Editor-in-Chief of the Canadian Mathematical Bulletin, 2014-2019
- Associate Editor of the Journal of Mathematical Analysis and Applications, 2007-present

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